System and method for a displacement measurement

ABSTRACT

System and method for profiling of a surface with lateral scanning interferometer the optical axis of which is perpendicular to the surface. In-plane scanning of the surface is carried out with increments that correspond to integer number of pixels of an employed optical detector. Determination of height profile of a region-of-interest that is incomparably larger than a FOV of the interferometer objective is performed in time reduced by at least an order of magnitude as compared to time required for the same determination by a vertical scanning interferometer.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation from the U.S. patentapplication Ser. No. 15/632,849, filed on Jun. 26, 2017 and nowpublished as US 2018/0003484, which in turn claims priority from andbenefit of the U.S. Provisional Patent Application No. 62/356,069 filedon Jun. 29, 2016. The disclosure of each of the above-identified patentapplications is incorporated by reference herein.

TECHNICAL FIELD

The present invention relates to systems and methods for non-contactprofilometry of surfaces and, more particularly, to lateral scanninginterferometric systems devoid of angular tilt intentionally introducedbetween the interferometric objective and the sample stage.

BACKGROUND

Production processes in micro- and nano-technology requires adequatemeasuring instruments to obtain three-dimensional (3D) geometries.Vertical scanning interferometry (such as scanning white-lightinterferometry, in one example) achieves a nanometer resolution/accuracyin the axial direction, and is particularly suited for the measurementof step height structures (for example, in micro-electro-mechanical,MEMS, structures). The measurement principle is based on a so-calledphase-shifting, or depth scan, or z-scan, during which the optical pathdifference between the measuring and reference arms of theinterferometer is varied in small steps. In the situations where thefield-of-view (FOV) subtended by the object/sample is substantiallyhigher than the FOV of the optical objective used with theinterferometer, or in situations where the dimensions of the sample areincomparably larger than the FOV of the optical objective, theusefulness of this approach is severely diminished, both due toimpractically-long times required for profiling of the whole sample, theerrors introduced at high numerical apertures, and the continuous needfor cumbersome stitching of images.

The methodology of lateral scanning white-light interferometry, whileallowing for a continuous data acquisition and substantially eliminatingthe need for image stitching, requires an angular tilt between theoptical axis of the objective and the normal to the sample surface,leading to a critical need in a regular stage tilt calibration.

SUMMARY

An embodiment of the present invention provides a method for profiling asurface with an in-plane scanning interferometer. The method includespositioning the surface perpendicularly to an optical axis of anobjective in a sample arm of the interferometer; and configuring areference arm of the interferometer to form interferometric fringes, atan optical detector of an optical system containing such interferometer.The fringes are tilted with respect to a chosen axis when the surface isilluminated through the sample arm. The method additionally includesacquiring optical data from a distribution of light formed at theoptical detector and containing the interferometric fringes while thesurface is being scanned along the chosen axis in a plane of thesurface.

Embodiments additionally provide a method for profiling a surface. Themethod includes determining a height profile of the surface from phasesof light distribution (formed in reflection of light by the surface withthe use of an in-plane scanning interferometer and containinginterferometric fringes that are angularly tilted with respect to adirection of an in-plane scanning of the surface), while the surface isbeing scanned in the direction perpendicular to an optical axis of asample arm of the interferometer. In each of the embodiments, a width ofan apodization curve, that limits the distribution of intensity of saidinterferometric fringes and represents a change in contrast of suchinterferometric fringes, can be optionally varied by modifying across-sectional profile of light delivered to the interferometer andused for measurements.

Embodiments further provide an apparatus for profiling a surface undertest, which apparatus includes (i) a beam splitter positioned to dividea light beam from a light source into a measurement light beam and areference light beam directed along a reference axis; and (ii) areference reflector positioned in an optical path of the reference lightbeam, the reference reflector being inclined with respect to thereference axis. Here, the beam splitter is configured to direct themeasurement light beam towards the surface to irradiate the surface andform a reflected measurement light beam, said reflected measurementlight beam passing through the beam splitter to interfere with thereference light beam upon reflection thereof from the referencereflector.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood by referring to thefollowing Detailed Description of Specific Embodiments in conjunctionwith the not-to scale Drawings, of which:

FIG. 1 is a schematic diagram illustrating a vertical scanninginterferometer device;

FIG. 2A is a schematic diagram of a data cube containing 3D datarepresenting an optical signal that describes the profile of the sampleunder test (SUT) obtained with a conventional vertical scanninginterferometer. Here, all individual image frames are aligned in x- andy-directions and each level of the data cube in the z directionrepresents a new, individual image frame;

FIG. 2B presents a plot schematically illustrating loss of contrast of asignal, acquired with the conventional vertical scanning interferometer,and caused by behavior of a cross-term of interference between themonochromatic optical waves propagating through the reference and sample(test) arms of the vertical scanning interferometer (This effectgenerally depends on the spatial extent of the illumination source inthe pupil of the microscope objective);

FIGS. 3A, 3B illustrate an embodiment of a scanning-light modulator(SLM) MEMS-based device;

FIG. 4 illustrates an embodiment of an in-plane scanning interferometricsetup of an embodiment;

FIG. 5A, 5B, 5C illustrate the repositioning of the sample under test(SLM) in a plane parallel to the plane of the sample under test inaccord with operation of the in-plane shifting interferometer of anembodiment of the invention;

FIGS. 6A, 6B illustrate a principle of data acquisition according to anembodiment of the present invention in which (in contradistinction withthe data acquisition of the vertical shifting interferometer, FIG. 2A,which provides only the phase-shift information representing a shiftalong the z-axis) both a phase-shift information and information about aspatial shift along the x-axis (in-plane shifting) are stored.

FIG. 7A illustrates interferometric tilt fringes registered by theoptical detector of an embodiment of the invention as a result ofjudicious tilt/tip of the reference reflector of the embodiment,required for the operation of the embodiment.

FIG. 7B illustrates the image of the SUT captured by a 1,000-by-1,000camera pixel section at a chosen location of the SUT during the in-planescanning;

FIG. 8A is a portion of an image of the surface height of the SLM-basedSUT, obtained as a result of the in-plane scanning of the SUT along a 1mm distance in x-direction;

FIG. 8B is a 25×25 square micron subsection (marked as SQ) of the imageof FIG. 8B;

FIGS. 9A and 9B illustrate first and second phase maps constructed basedon interferometric measurement of the same surface of the SUT with anembodiment of the invention but respectively started at first and secondlocations separated from one another, along the direction of in-planescanning (x-axis) by one increment of the in-plane shift along thex-direction;

FIG. 9C illustrates a third phase map resulting from the subtraction ofthe map of FIG. 9B from the map of the FIG. 9A;

FIG. 10 is a contour plot illustrating the phase error present acrossthe image of the SUT, acquired during the operation of the in-planescanning interferometer of the embodiment and caused by the wavefrontmismatch between the two arms of the interferometer;

FIG. 11 is a plot illustrating the capability of an embodiment of theinvention to track the deviation of a portion of the surface of the SUTthat is being measured at the moment from the ideal location at thefocal plane of the objective of the test arm of the in-planeinterferometer;

FIGS. 12A, 12B, 12C illustrate a related embodiment equipped with anoptical obscuration element configured to increase contrast ofinterferometric fringes formed during the operation of an embodiment;

FIG. 13 illustrates an example of a lithographic exposure apparatus inline with which an embodiment of the present invention can be employed.

Generally, the sizes and relative scales of elements in Drawings may beset to be different from actual ones to appropriately facilitatesimplicity, clarity, and understanding of the Drawings. For the samereason, not all elements present in one Drawing may necessarily be shownin another.

DETAILED DESCRIPTION

Examples of embodiments of the present invention, discussed below,disclose methods and apparatus for a novel in-plane scanninginterferometric technique the use of which facilitates surfaceprofilometry and, in particular, a displacement of repositionableelements of the surface thereby enabling a verification of operabilityof a MEMS-based device without a need in measurement-related calibrationof the measurement apparatus itself.

(1) Operational Considerations Arising with the Use of RelatedPhase-Shifting Interferometric Measurement Systems and Addressed by theImplementations of the Present Invention.

A tool employing a vertically-scanning interferometer 110 (shownconfigured as a Linnik interferometer) with well-aligned optics (shownschematically as 100 in FIG. 1) is often used for phase-shifting-basedprofiling of a reflective surface 100 (referred to as surface undertest, or SUT). Such a measurement tool, however, is subject to a rathersubstantial practical limitation. It requires optically-well-matchedmicroscope objectives 104, 106 in reference and test arms of theinterferometer (the latter containing the SUT 100), that is objectivesthe optical aberration characteristics of which are similar orsubstantially equal. Moreover, such measurement tool requires thepresence of a reference reflector (REF, 120) in the reference arm; theREF has to be optically (meaning, after accounting for the possiblespatial fold at the beamsplitter 122) parallel to the SUT 100. At thesame time, many objectives in practice—and especially those used forqualitative and not quantitative measurements—are known to havesubstantially high aberration content and, therefore, are unlikely to beoptically matched to a degree required for use in a well-balancedvertical scanning interferometer.

In a z-axis phase-shifting operation of a vertical scanninginterferometric setup, a beam L from the light source is collimated anddivided into a measurement (sample, test) beam 140 and a reference beam142 by a beam splitter. The light reflected from the reference andsample surfaces is then combined, and the image is projected onto a 2Dimaging detector (such as a CCD, for example; not shown) forregistration and further processing with a data-processing electroniccircuitry (not shown) to form a 3D signal of FIG. 2A, representing aprofile of the SUT. The detector registers multiple images ofdistributions of irradiance of light formed at the surface of thedetector in time while the phase between the reference beam of light 124(returned by the reference reflector 120, often a flat mirror) and themeasurement beam 128 propagating through the interferometer 110 is beingmeasured.

The conventionally-configured surface profile measurements possessseveral substantial shortcomings:

On the one hand, in order to reach high spatial resolution along thez-axis, some sort of phase scanning or phase shifting is required. As aresult, the phase-shifting must be complemented with very small periodicreversible motions or displacements introduced between the referencereflector 120 and the SUT 100 along a direction of incidence of themeasurement beam of light (optical axis or z-axis). Such motions ordisplacements are often introduced by making the reference mirror 120shift (or “step”) in step-increments on the order of 75-100 nm perincrement or so over a distance of hundreds of microns in a directiondefined to be transverse to the surface of the reference mirror (forexample, along an optical axis 130 as shown with an arrow 132).Alternatively, the stepping or scanning of the SUT 100 along the opticalaxis 130′ is used to achieve the same result. The optical aberrations ofthe objective(s) 104, 106 cause the retracing of errors of themeasurement as well, which in the simplest case implies that the resultsof the phase-shifting-based measurement performed with the tool 110contains a spatially-varying error of the SUT 100 topography, whichspatially-varying error may depend on the shape of the measured part100. While calibration of the conventionally-structured phase-shiftmeasurement with the tool 110 can be performed, it is known in the artto be quite involved and difficult and desired to be avoided ifpossible.—Another operational shortcoming of using the conventionalvertical-scanning-interferometer-based phase-shifting profiling toolstems from the fact that it is almost a given that the transversedimensions of the SUT 100 are substantially larger than thefield-of-view (FOV) of the objective (104, 106) used in theinterferometer. For a numerical aperture, NA, of about 0.7 the resultingFOV of the objective might be only about or on the order of 300 micronsby 300 microns, for example. When a larger sample needs to be measured(with a surface the dimensions of which are at least twice or more aslarge as the FOV of the objective in one example; or at least one orderof magnitude larger than the FOV of the objective in another example, orat least two orders of magnitude larger in yet another example), itstotal area is typically operationally “split” or “subdivided” into anumber of overlapping regions that are measured independently, and thenstitching techniques are implemented to reconstruct the entire surface.For example, when the SUT 100 is tens or hundreds of millimeters across,in order to profile the SUT it must be scanned in the xy-plane (in aplane of the reflective surface being measured), which is perpendicularto the optical axis 130, 130′ along which the relative shift between thereference reflector and SUT is introduced to collect phase-shiftingoptical data conventionally. As a result, the SUT-profiling procedureincludes in-plane scanning of the SUT 100 in spatial increments on theorder of several hundreds of microns over a distance exceeding tens ofmillimeters while, at the same time, performing multiple “stepping” in az-direction at each of the incremental position of the scan. At aminimum, this causes the overall time, required to complete theacquisition of the phase-shifting optical data, to be impracticallylong. For example, in a case of a reasonably limited (in terms ofz-profile) SUT, it may be assumed that a typical vertical-scanningcommercial system can probably perform a vertical scan in under 10seconds (for example, in 7 seconds). Stepping in x-and-y takes anotherfew seconds (for example, 3 seconds). Based on these practicallyjustified assumptions, to complete a process of scanning of a 10×10 mmregion of an SUT with a 0.3 mm×0.3 mm of the actual objective FOV(which, in practice is reduced to about 0.25 mm×0.25 mm of the effectiveFOV because of the practically-unavoidable spatial stitching overlaps)about 4.50 hours or more are required.

Yet another important aspect of the measurement optical signal acquiredwith the use of a conventional phase-shifting interferometric setup isthat intensity of the interference fringes (formed as a result ofoptical interference between the test and reference beams returnedthrough the objectives 104, 106 to the optical detector) are multipliedor apodized by a curve representing a degree of coherence of light Lused for the measurements. (Such an apodization curve may be referred toas a “coherence envelope”). Indeed, contrast of the registered by thedetector signal, which results from the interference between the sampleand reference beams of light, is proportional to the modulus of thecomplex degree of the mutual coherence of the corresponding opticalwavefronts. Because of the limited spectral bandwidth of light L, theinterference can occur only in a limited space about a coherence planedefined by the zero optical path differences. This property usually isused for retrieval of the sample's height or topography.

The apodization with the “coherence envelope” changes the fringecontrast as a function of a relative z-displacement between thereflectors 110, 120 because the various sections of the high-NA samplebeam 140 are incident onto the SUT at angles varying from, for example,0 degrees to 37 degrees (for NA=0.6 of the objective 104) or even up to45 degrees (for NA=0.7). As a result, a z-displacement increment ofΔz=100 nm on optical axis 130 causes a displacement of about Δz/cos(asin(NA)), or about 141 nm along a direction corresponding to an angle ofNA of 0.7. The integration of optical data acquired by the detectorwithin the angular range from 0 degrees to 45 degrees inevitably causesloss in contrast that limits the coherence envelope for a monochromaticsource of light L. A schematic example of this loss in contrast is shownin FIG. 2B, showing a behavior of a cross-term of interference betweenthe monochromatic optical waves propagating through the reference andsample (test) arms of the vertical scanning interferometer of aphase-shifting measurement tool, for a NA=0.6 objectives 104, 106. SomeSUT samples may include such surface height discontinuities that onepart of the SUT surface relative to another part of the SUT surfacesimply cannot be determined, because the number of fringe cycles cannotbe determined from a fringe image. This practical situation is oftenreferred to as a 2pi phase ambiguity. The coherence envelope (an exampleof which is shown in FIG. 2B) has different contrast for each fringe indepth, and this information can be used to determine how many integerfringes there are between the two sides of a step. However, in manypractical situations, such as the measurements of MEMS-devices discussedbelow, the user knows a priori that the total change-in-height of thesurface discontinuities is limited to less than one-quarter of awavelength of used light. A person of skill in the art, therefore, wouldappreciate that (considering the sampling theorem factor of 2 and theadditional factor of 2 coming from the measurements carried out inreflection), no 2pi phase ambiguities is encountered during themeasurements of such MEMS-based SUT. Put differently, the “coherenceenvelope” is much shorter for a high-NA beam than it is for a low-NAbeam. In addition, the distance the substrate 100 must be moved tointroduce a desired phase shift is different for light coming in atdifferent angles, which is the cause of the coherence envelope narrowingthat can be observed with a higher NA beam.

While these effects of loss in contrast and inconsistency (ordifference) among the z-motion increments required for light coming atdifferent angles as related to the measured interferometric signal maybe viewed as acceptable for low-NA situations, under particularcircumstances these deficiencies become operationally inadmissible. Inparticular, for applications where the SUT possesses surface featuresthe imaging/profiling of which requires the use of objectives with NAhigh enough to bring to life the deficiencies of theconventionally-configured vertical scanning interferometer (such as, forexample, NA of 0.6 or higher), these effects become serious practicalimpediments, especially when and if such SUT has a continuous(uninterrupted) or quasi-continuous surface or a surface that is“discretized” in a certain fashion. Embodiments of the present inventionprovide a solution that avoids and/or addresses these problems.

Accordingly:

One operational limitation of related art, solved by the presentinvention, stems from the fact that a conventionally-used verticalscanning phase-shifting interferometric modality employs a principle ofperiodic stepping or repositioning between the measured and referencesurfaces in a direction perpendicular to the measured surface (referredto herein as z-stepping or z-scanning, for short) at each and everychosen location at the measured surface that is placed withouttransverse displacement within the FOV of the used objective during thewhole duration of z-stepping procedure. Such z-stepping, repeatedmultiple times across numerous locations at the measured surface,requires an impermissibly-long time to spatially profile a reflectivesurface. Such typically-required impermissibly-long profiling time isreduced at least by an order of magnitude or more with the use of apresently-discussed metrology system of configured (i) to effectuate aphase-shifting measurement as a result of an “in-plane” repositioning orscanning of the measured surface (i.e., repositioning in the plane ofthe measured reflective surface) along a chosen scanning axis lying insuch plane and (ii) to register interferometric fringes that are formedat a surface of an optical detector (at least in part due to opticalinterference of measurement light reflected from the reflective surfacewith reference light) and that are tilted or inclined, in such plane,with respect to the chosen scanning axis.

Another operation problem manifests in a specific case, when thereflective surface that is being measured with a conventionalphase-shifting modality represents a surface of a spatial lightmodulator (such as that based on a MEMS device, for example) and isformed by an array of mirror elements (each with side dimensions on theorder of a couple of microns by a couple of microns) that are configuredto move in a direction transverse to the surface of the array (andreferred to as a displacement direction). This operational problem iscaused by lack of knowledge of whether displacements of such mirrorelements are changing over time in a pre-determined (according to adesign) fashion or, to the contrary, in an unpredictable fashion. Thisproblem is solved with the use of a presently-discussed metrologyinstrument that employs an optical interferometer configured toeffectuate a measurement based on a phase-shifting technique that iscarried out in absence of any relative movement between the array of themirror elements and the interferometer along the displacement directionand, instead, is carried out only due to the relative in-plane movement(that is, a movement along a plane of the array).

Examples of a continuous surface with a complex profile subtending largeFOVs—(such as surfaces of, for example, CCD or CMOS sensors withmicron-sized pixels over an area that is many millimeters on a side, orsurfaces of DLP chips for use in projectors, or surfaces of biologicalchips for parallel processing of DNA samples, or surfaces of smallaspheric lenses) are well familiar to a person of skill in the art, anddo not require any particular discussion.

Specific examples of a surface that is discretized and almostnecessarily requires a high-NA optics may be found, for instance, in theapplications of a lithographic exposure tool or digital scanner, when aconventionally-used fixed-pattern mask or reticle that travels on areticle-stage is replaced with a MEMS device such as one containing anarray of mirror elements (also referred to herein as a mirror array orspatial light modulator, SLM). The surface of such mirror array isdiscretized into individual mirror elements. Dimension of a SLM-basedphase-mask in a lithographic exposure tool may be as large as about 500mm×15 mm in one example, and the FOV subtended by such SLM is muchlarger than a FOV of a typical microscope objective utilized in avertical scanning interferometer. Mirrors in the array may be configuredto move or reposition discretely or continuously along a line transverseto a surface of the device between the two extreme positionscharacterized by two corresponding height values with respect to achosen reference level. The two height levels may be chosen to ben-phase apart at a given wavelength of light incident onto a givenmirror of the array, thereby defining the whole array of the mirrors tooperate as a phase mask. While such MEMS device (configured as a phasemask or reticle with respect to light incident upon it) may be fixed inplace, it may be programmed to move a spatial pattern of distribution ofindividual mirror(s) across the mirror array, for example in a fashionsynchronized with the motion of the wafer in the exposure tool. Should amirror element fail, the pattern of the phase mask changes as comparedto the desired or pre-determined pattern, and should not be transferredto (printed on) the wafer. Understandably, the ability to measure thephase (or displacement) of each individual mirror element of such phasemask to determine if it is working properly, both “on” and “off” of thedigital scanner, is of operational importance.

FIGS. 3A, 3B illustrate schematically a particular non-limiting example300 of an SLM containing an array of individual mirror elements each ofwhich includes an upper mirrored or simply reflective surface (314A,314B, 314C) and a lower electrode surface. The transverse translation ofan individual mirror can be effectuated, for example, based on theprinciple of electrostatic attraction and/or repulsion between anindividually-addressable electrode with which a given individualmicro-mirror is equipped and a based electrode that is common to all themirrors of the device 300. The individual electrode 320C of the mirror314C and the base electrode 322 provide but one example of theimplementation of such concept. In this example, by applying anappropriate difference of potentials between the electrodes 320C, 322sufficient to create an electrostatic force that overcomes the tensionalload provided by mechanical resistance of a spring 326C juxtaposed withthe mirror 314C, the mirror 314C is caused to move towards the baseelectrode 322.

Depending on particular details of the structural implementation of theembodiment 300, such movement may be effectuated, for example, in asliding fashion provided by a sleeve 332C encircling the fixedsupport-pole 330C and, optionally, connected to the spring 326C such asto increase the potential energy stored in the spring 326C. In anotherexample (not shown), the pole 330C may be configured as a componentaffixed to the micro-mirror 314C and moveable with respect to theelectrode 322, in which case the movement of the micro-mirror 314C maybe coordinated with the corresponding movement of the support-pole 330Cin a piston-like fashion, transversely to the device surface 316. Otherimplementations of an individual micro-mirror direction-reversibletranslation in a direction transverse to the surface of thephase-modulating embodiment of the invention can be readily envisionedby a skilled artisan.

In a specific situation where the incident light 310 has a wavelength ofabout 193 nm, a dimension of a given micro-mirror 314A, 314B, 314C maybe on the order of a few microns (for example, of about 2 microns by 2microns, or 4 microns by 4 microns, or 6 microns by 6 microns), and themaximum range transverse displacement A may be on the order of 40-50 nmor so. In operation, a phase-modulating embodiment such as theembodiment 300 of FIGS. 3A, 3B, imparts variable across the lightfront(light wavefront) 310 phase-shift as a function of a voltage levelcorresponding to such micro-mirror.

(2) Examples of Embodiments of the Measurement System of the Invention

The idea of the invention stems from the realization that a surface of alarge (multiply-exceeding the FOV of the used optical objective) samplecan be spatially profiled (with a resolution on the order of 1 nm orbetter—in one implementation, measured as 0.14 nm 1σ—along a z-axisnormal to the surface) with an interferometric set-up configured to scanthe SUT along the plane of the SUT and in absence of any phase-shiftingoperation or activity (as defined in the art) effectuated along thez-axis or an axis transverse to the plane of the SUT. Such in-planescanning interferometer is configured to form, across the sensitivesurface of the optical detector, interferometric fringes that arejudiciously tilted with respect to the direction of the in-planescanning. The non-zero angle of tilt or inclination between theinterferometric fringes and the direction of lateral scanning of thesample in a plane of the sample surface is either acute or obtuse(depending on the point of view). In other words, the angle formedbetween a vector that is collinear to the direction of motion of the SUTin the image of the surface of the SUT formed at the detector, and aline representing constant optical path difference between the test andsample arms of the interferometric set-up used in an embodiment of theinvention has a non-zero value.

In the example of FIG. 4, the embodiment 410 of an in-plane scanninginterferometric setup is shown configured in a fashion similar to thatof the Linnik interferometer structure. Here, the reference mirror 420of the in-plane scanning interferometer 400 is intentionally andnecessarily tilted about the y-axis and with respect to the optical axis130, 130′ (the axis perpendicular to the SUT) such as to form at least1.5 full-period interferometric fringes across the surface of theoptical detector at a non-zero angle with respect to the direction ofin-plane scanning (shown as x-axis in this example). Such tilt fringesacross the FOV are used to introduce the desired phase differencebetween the neighboring areas of the SUT. The angle of tilt of thereference surface (reflector) 420 about the y-axis is shown as A betweenthe normal 404 to the reference surface 420 and the local optical axis130. It is appreciated that a differently-configured interferometricsetup can be used for the same purpose, such as a Michelson setup or aTwyman-Green setup, to name just a few.

The structure and operation of the embodiment 410 (and, in particular,the reflector 420) is devoid of and does not employ a z-stepping orz-scanning capacity (as defined herein, during the instantaneousmeasurement of a chosen location of the SUT) or phase-shifting operation(along the z-axis as understood in the art). Instead, it is equippedwith an appropriate (electro)mechanical means (such as a piezo-based orotherwise configured micropositioner 444) configured to move, forexample, the SUT 100 along a plane of the SUT 100 (“in-plane scanning”with respect to the SUT) in the scanning direction of the x-axis, asindicated with an arrow 444A. (In the alternative, the interferometricsetup 410 as a whole can be moved with respect to a fixed SUT 100, whichdoes not change the principle of operation of the embodiment). At thesame time, the embodiment 410 may be equipped with an appropriaterepositioner configured to slowly and, optionally, contemporaneouslywith the in-plane scanning motion 444A change a position of the SUTalong the z-axis at a speed comparable with or even slower than thespeed of in-plane scanning. Such capability to track the change ofprofile of the continuous or quasi-continuous SUT becomes useful toensure that the instantaneously-measured location at the surface of theSUT remains within the depth of focus (DOF) of the objective 104,because the SUT is scanned in the x-direction across a distanceexceeding the typical instantaneous field of view of the measurementsystem by at least 10 to 100 times or more. Since the alignment of theSUT with respect to tip and tilt, necessary to keep the surface of theSUT within the limited focal range of a high NA optical system, islikely to become about 100× tighter (if the overall, operational FOV isextended by 100× as a result of the scanning employed here), theproposed technique mitigates the risk by moving the sample inz-direction as it scans in-plane (along the x-direction) to keep thefringes in approximately the same location all the time. A skilledartisan readily appreciates that such capability simply does not qualifyas and is different from the phase-shift-enabling z-scanning capabilityof vertical scanning interferometers of related art. Moreover, suchz-movement is effectuated after the informational feedback is alreadydetermined from the interferometric images and is not predetermined;further, the accuracy level of such z-movement is on the order of 50 nmor so and is simply insufficient to support the piezo-basedphase-shifting, that requires the accuracy of below 1 nm.

(3) Scanning of an SUT.

In addition to addressing problems associated with the vertical scanningwhite-light interferometric profilometry discussed above and, notably,in advantageous contradistinction with related embodiments of lateralscanning interferometers, an embodiment of the invention requires thatthe local optical axis 130′ be substantially normal—and not tilted—withrespect to the surface of the SUT 100 to avoid considerable shortcomingsof operation, almost inevitably present otherwise, as would be readilyunderstood by a person of skill. (Phrased differently, in an embodimentof the invention there is no angular tilt between the interferometricobjective and the sample stage). In particular, the operation of arelated device in the situation when the axis 430′ and the normal tosurface of the SUT 100 are not substantially parallel to one another, aswill be readily appreciated by a skilled artisan, the use of the deviceat high levels of optical magnification (in one example—above about100×, when a typical objective may have a working distance of 1 mm orless) required in practice becomes extremely limited if not impossibledue to the prospect of mechanical interference between the sample andthe microscope objective (the latter typically having a small workingdistance at high magnification and high NA). Furthermore, at the edgesof the FOV of the objective 104 in such situation the surface beingmeasured ends up out of focus, as a result of which the spatialresolution of in-plane scanning is sufficiently sacrificed. Moreover,the measurement system responds differently to spatial changes in localslopes (inclinations) of the surface of the SUT 100 depending on thesign of such changes (that is, whether the slopes are upwards ordownwards, positive or negative) due to the overall tilt of theinstrument. When the axis 430′ and the general normal to the surface ofthe SUT 100 are not substantially parallel to one another, themeasurement technique described in related art simply cannot accommodatethe unwanted motion of the SUT along the z-axis during the lateral scan,unlike that described in the present application. (Specifically, therelated art describes setting the system up so that there is a knownphase shift between measurements of a given SUT location as it movesacross the FOV of the objective of the interferometer. Thedata-processing algorithm(s) of the related art require a consistentphase step, and produce an error each time an “unwanted” motion alongthe z-direction would cause a different phase step, or operationalinconsistency.) Additionally, unlike lateral white-light scanninginterferometers of related art, for example (where the exact sampleprofile can be recovered only if the angle of tilt between the samplestage and the interferometric objective in known accurately because theheight of a sample surface varies linearly with the tangent of the tiltangle), embodiments of the present invention is free of the need for atilt angle calibration required by each measurement.

In a specific implementation, when the SUT includes an array of mirrorscomprising an SLM device, the reference reflector may be inclined withrespect to the optical axis 430 such to form interferometric fringestilted with a slope corresponding to about π/2 phase between theneighboring mirror elements of the array of mirror elements. In aspecific case, when the SUT 100 includes an array of 4-by-4 micronmirror elements or pixels (such as elements 314A of FIG. 3A, forexample), and for light L at a wavelength of λ=650 nm, such as slopecorresponds to about 81 nm of optical-path difference between theimmediately neighboring SLM pixels, and to A ˜0.58 degree. In adifferent implementation, the tilt angle of interferometric fringes canbe chosen to correspond to λ/8 (A ˜0.29 degree).

In one example, if a CCD pixel has an actual side dimension of about 200nm (in the optical space occupied by the SUT, interchangeably referredto as “object space”), then each of the individual SLM mirror elementsof a 4×4 square microns is measured by 20×20 CCD pixels at each imageframe. In order to measure a z-position (position along an optical axis)of an individual mirror element, during the operation of the embodimentthe SLM (SUT) 100 is translated (scanned) along the plane of the mirrorarray with the use of positioner 444 in the direction of the tilt offringes (x-axis, direction of in-plane-scanning) as images are capturedsuch that an increment of an in-plane translation of the SUT 100corresponds to an integer number of the pixels of the CCD camera(optical detector). This is schematically shown in FIG. 5A, 5B, 5Cillustrating three sequential positions of the SUT (in this case, theSLM 510), shifted with respect to one another in-plane of the SUT alongthe x-axis by the distance d (chosen, in this example, to be equal to aside-dimension of an SLM pixel or an individual mirror element of theSLM). Here, the grid 510 represents an array of individual mirrors ofthe SLM and each of the squares 510A of the grid 510 represents oneindividual mirror of such array. A full interferometric tilt fringe,formed at the optical detector and shifting its position in relation tothe position of the array 510, is shown as 520. (If there is no z-motionof the SUT, then the fringes stay at the same location relative to thecamera pixels during the x-scan.) In this example, the interferometricfringes are tilted with respect to the scanning direction x by about 90degrees. As the in-plane scanning procedure progresses across the wholex-range of the SLM device with in-plane incremental shifts such thateach SLM mirror element (one of which is shown as the element 524) ismeasured with different pixels of the CCD camera, each of which islocated along the same row of pixels of the CCD camera. As a result, achosen element of the SUT traverses the entire FOV while being measuredwith light incident thereon at a variety of phases due to the tilt ofthe reference reflector 420.

Depending on a particular implementation, the measurement of theoperational states of the SLM mirror elements in their discreetpositions can be done in any of at least three ways: a) switching orchanging the operational state of the SLM between the discreet positions(state ‘A’ and state ‘B’) at every position (each x-location) of theinterferometer above the SUT while such position is fixed (that is,during a given in-plane scanning step), thereby taking two measurementsat each location of the raster scan of the SLM, or b) completing thefull raster scan of the SLM being in one state (e.g., state ‘A’),shifting the SLM mirror states (into state ‘B’), and then repeating thewhole process, or c) changing the state of the SLM between two statesbetween every two consecutive camera frames, so that the odd numberedcamera frames correspond to state ‘A’ and the even numbered camera framecorrespond to state ‘B’, as the SLM is scanned at a constant velocity.

As a result of such sequential measurements, the 3D cube 600 of opticaldata is acquired, as shown schematically in FIGS. 6A, 6B in which (incontradistinction with the data cube of FIG. 2A that is acquired duringthe conventional measurement and containing only a phase-shiftinformation) both a phase shift information and information about aspatial shift along the x-axis are stored. Such data mapping can beimplemented with the use of, for example, a least-squares phaseestimation algorithm (sometimes referred to in the art as a LSPSIalgorithm). As illustrated in FIG. 6A, for example, each of theindividual data frames represents the profile (of the SLM sample undertest) that is shifted by an in-plane spatial-shifting increment d withrespect to the profile represented by an immediately preceding orimmediately following data frame. Here, d corresponds to an integernumber of camera pixels (after taking the magnification of the opticalsystem into account). Since the dimensions of each of the individualdata frames are the same, the data cube is constructed as a result ofalignment of multiple mutually-shifted data frames.

A distribution α_(i)(x,y,t) of the SUT-profile is found for each cameraframe (image frame) and a best-fit plane (θ_(x), θ_(y), z), described bytip, tilt, and a mean z-value, is also found for each image frame. Thisdistribution represents the path of the SUT through space as it scans(is scanned) in-plane (with results being fed into the LSPSI algorithmto improve the estimates of the actual phase shifts used during datacollection, which in turn improves the resulting determination of thephase map shown in Equation 4, below). The value of α_(i)(x,y,t) iscomputed for every frame and every pixel in the data cube; this value isbased on the expected trajectory of the SUT as well as the changes thatare measured during data collection by assessing each camera frame todetermine (θ_(x), θ_(y), z) as a function of time. The B-matrix elementsare computed as weighted sums of the measured irradiance I of light

$\begin{matrix}{B = \begin{bmatrix}{\sum I_{i}} \\{\sum{I_{i}\cos \; \alpha_{i}}} \\{\sum{I_{i}\sin \; \alpha_{i}}}\end{bmatrix}} & (1)\end{matrix}$

and the A-matrix elements are computed as

$\begin{matrix}{A = \begin{bmatrix}N & {\sum{\cos \; \alpha_{i}}} & {\sum{\sin \; \alpha_{i}}} \\{\sum{\cos \; \alpha_{i}}} & {\sum{\cos^{2}\alpha_{i}}} & {\sum{\cos \; \alpha_{i}\sin \; \alpha_{i}}} \\{\sum{\sin \; \alpha_{i}}} & {\sum{\cos \; \alpha_{i}\sin \; \alpha_{i}}} & {\sum{\sin^{2}\; \alpha_{i}}}\end{bmatrix}} & (2)\end{matrix}$

where N is the number of measurement values at a given location of theSUT.

The phase y (and, correspondingly, physical height) of a surface featurecan then be determined from the vector

$\begin{matrix}{a = {\begin{bmatrix}a_{0} \\a_{1} \\a_{2}\end{bmatrix} = {A^{- 1}B}}} & (3) \\{{{as}\mspace{14mu} \tan \; \phi} = {a_{2}/{a_{1}.}}} & (4)\end{matrix}$

It is understood by a person of skill in the art, therefore, thatembodiments of the invention provide an apparatus for profiling an SUT.Such apparatus includes, in its simplest form, a beam splitterpositioned to divide a light beam from a light source into a measurementlight beam and a reference light beam directed along a reference axis;and a reference reflector positioned in an optical path of the referencelight beam, the reference reflector being inclined with respect to thereference axis. The beam splitter is oriented to direct the measurementlight beam towards the SUT to irradiate the SUT and to form a reflectedmeasurement light beam directed to pass through the beam splitter tointerfere with the reference light beam upon reflection thereof from thereference reflector. In a specific case, a normal to the referencereflector crosses the reference axis. The apparatus also includes ameasurement objective disposed between the beam splitter and the SUT toconverge the measurement light beam incident onto the measurementobjective from the beam splitter; and a reference objective disposedbetween the beam splitter and the reference reflector to converge thereference light beam incident onto the measurement objective from thebeam splitter. The apparatus further includes a positioner (in operablecooperation with at least one of the apparatus and the SUT) that isconfigured to change a positional relationship between the apparatus andthe SUT at least in a chosen direction (and, in a specific case, to movethe SUT at least in such chosen direction). An axis normal to thereference reflector lays, in one specific implementation, in a planethat contains both the reference axis and the measurement axis. In arelated implementation, the first direction is defined by a vector thatlays in the same plane. In addition, the apparatus includes a detectorconfigured to detect light distribution formed as a result of opticalinterference between the measurement light beam and the reference lightbeam. Alternatively or in addition, the detector may be configureddetect such light distribution while the positional relationship isbeing changed.

(4) Examples of Empirical Results

In one implementation, an in-plane scanning interferometric setupdiscussed in Secs. (3), (4) was built using two optically-matchedobjectives 104, 106 with NAs=0.6. The reference surface 420 was tiltedabout the y-axis to introduce tilt fringes (in a related embodiment,additional tilt of the reference surface 420 about x-axis may also beintroduced).

The temporal coherence of the light source chosen for the experimentalsetup is preferably long enough to maintain contrast over the tilt rangeacross the FOV, or at least across a large section of the FOV. In oneimplementation, a commercially-available LED generating light at about650 nm provided light L with operationally-sufficient characteristics.In another implementation, a light source included a superluminescentdiode (SLD) with a spectral bandwidth of about 8 nm to 100 nm FWHM, thelight output from which was coupled into a single-mode optical fiberwith a core diameter of about 4 microns, providing temporal coherencelength of about 40 microns for light delivered to the experimentalsetup.

An example of an image of an area of the SLM sample under test,positioned in the embodiment of the in-plane-scanning interferometeraccording to the idea if the invention with the reference reflector 420appropriately aligned in tip and tilt (as evidenced by the clearlyvisible tilt interferometric fringes, required for the measurementaccording to the idea of the invention) under illumination L deliveredfrom the He—Ne laser source, is shown FIG. 7A. Following the alignmentof the interferometer, the SLD source (λ=650 nm) was employed to set theoptical path difference along the z-axis between the SUT 100 and thereference reflector 420 to ensure such OPD is below the coherence lengthof the SLD-generated light. In some situations it may be beneficial tochoose the light source with a relatively low coherence length to reducethe number of coherent stray beams of light and diffraction effects thatotherwise may be registered by the optical detector during the operationof the embodiment and increase the optical noise irrelevant for thepurposes of the measurement of the SUT. The SUT 100 (configured as theSLM with individual square mirror elements having side dimensions of 4microns in object space) was then translated incrementally, as discussedin Sec. (3), in the direction of the tilt (x-axis), by a known integernumber of optical camera pixels between each measurement, such that eachlocation on the SLM surface was measured multiple times with a varietyof fringe phases (as discussed above in reference to FIGS. 5A, 5B, 5C,6A). Notably, for the embodiment of the invention to operate, the phasesteps in x-direction do not have to be of a particular value as long asthe value(s) of phase step(s) is/are known, thereby providing a clearadvantage over and lifting an important operational limitation of thevertical scanning interferometer(s). However, it may be preferred toavoid in-plane stepping in x-direction in exact integer multiples of pi(in a case this precaution is not taken, the multiple measured valueswould correspond only to 2 different irradiance values and there may benot enough information available to calculate the phase associated witha point at the SUT surface). Notably, the actual values of the in-planephase steps can be found from the images acquired with the opticaldata-acquisition circuitry of the embodiment.

During the in-plane scanning in the x-direction, camera images werecaptured at a constant sampling rate. Here, the x-shift accuracyrequirement was measured to be within the range and on the order of 50nm to about 100 nm, which is at least one to two orders of magnitudeless restrictive than that of a conventional vertical scanning(z-phase-shifting) interferometer. It is noted that, incontradistinction with the white-light interferometry, which measuresthe peak of the coherence envelope (apodization envelope) of theinterferometrically-formed light distribution at the optical detector,an embodiment of the present invention is based on the measurement ofcontrast of interferometric fringes (corresponding to optical pathdifference of zero between the reference and test beams 142, 140). Morespecifically, an embodiment of the present invention is configured todetermine the surface position based on pre-determination of phaseinformation about interferometric fringes formed as a result ofoperation of the employed optical system.

In one implementation, the optical data were collected with the in-planeincremental shift corresponding to either 17 or 34 camera pixels perframe. For simplicity, a 1,000-by-1,000 camera pixel section of eachimage was used at each location of the SUT during the in-plane scanningin the LSPSI algorithm, an example of which section is show in FIG. 7B.In the example of FIG. 7B, the in-plane shift of 34 camera pixelsamounted to approximately 29 measurement data points for each ofin-plane increment locations of the SUT. It was empirically discoveredthat for a typical exposure time of about 1 microsecond and a rate of 15fps, the time increment between consecutive frames was about 66 ms andthe resulting image blur due to integration of the signal in the scandirection during the typical exposure time of about 0.05% of a size ofan individual camera pixel was practically negligible.

In a related example, the analysis of the optical data, collected viaoptical projection of each of the 4-micron-per-side SLM-based SUT pixelsonto an area of about 17-by-17 camera pixels, produced phase maps ofsuch SUT. An example of an portion of one of such phase maps is shown inFIG. 8A. In this experiment, the full distance of the SUT scanned alongthe x-direction was about 1 mm, which took about 15 seconds due to thehigh sampling density (number of data points) and low frame rate. TheFOV of the objective 104 was about 300 microns at the SUT.

While the +x and −x edges of the image appear to be noisy due to thelimited amount of data points taken at the beginning and end of thescan, such artifact does not change the principle of operation oroperability of the embodiment(s) of the invention and, in practice, iseasily solved by scanning beyond the limiting edge (or boundary) of theSUT. The height of the surface of the SUT in nanometers may be assessedfrom the color-bar of FIG. 8A. However, the smaller, 25-by-25 squaremicron area of the same image shown in FIG. 8B provides a betterassessment of the phase map and evidences that the measured height ofthe SLM elements is about 48 nm. (It would be appreciated by a skilledartisan that that the absolute value of the height of the surfaceelement derived from a phase map generally depends on the meanwavelength of the employed light source.)

Overall, in this embodiment a surface profile of an approximately 16×16mm² area of the SUT (configured as an SLM similar to that described inreference to FIGS. 3A, 3B) was measured with sub-nm axis (z) resolutionand sub-micron lateral resolution in about 15 seconds.

It is appreciated that in a related implementation of the measurementprocess, two scans of the same SUT can be performed, onespatially-shifted with respect to another by a distance corresponding toa predetermined number of in-plane shift increments (in this example, byan odd number of 17 camera pixels, or 1 individual mirror element on theSUT) to obtain two phase maps of the SUT. A subtraction of the imagerepresenting one of these two phase maps from the image representinganother phase map facilitates an assessment of the phase differencebetween neighboring elements of the SUT. In the case of the SLM-basedSUT of this example (the mirror elements of which could be in only twoheight states: either at 0 nm height or at 48 nm height), theimplementation of such related measurement empirically proved that thedifference between one SLM element and its neighbor was described by oneof 3 operational states: +48 nm, 0, or −48 nm.

The empirically obtained first and second phase maps of an area of theSUT are illustrated in FIGS. 9A, 9B, while the phase map representingthe subtraction of the second map from the first map is shown in FIG.9C. The subtraction of the first and second phase maps provides thedifference between neighboring SUT mirror elements.

Referring again to the measurements described in reference to FIGS. 8A,8B, 9A, 9B, 9C, the standard deviation of the height measurement of thesurface of the SUT can be computed based on the examination of a grayarea of the surface (such as, for example, any of areas 810A, 810B)across which the surface is substantially flat and no phase differencecan be measured over the distance corresponding to several SLM pixelelements.

In practice, the standard deviation 1σ was measured to be about 2.3 nmat a single camera pixel. The repeatability of an SLM height measurementis then determined as

${1{\sigma/\sqrt{{area}\mspace{14mu} {of}\mspace{14mu} {camera}\mspace{14mu} {onto}\mspace{14mu} {which}\mspace{14mu} {an}\mspace{14mu} {SLM}\mspace{14mu} {pixel}\mspace{14mu} {is}\mspace{14mu} {imaged}}}} = {{1{\sigma/\sqrt{17*17}}} = {{2.3\mspace{14mu} {{nm}/17}} = {0.136\mspace{14mu} {{nm}.}}}}$

Referring again to the phase map of FIG. 8A, the experimentally observedroll-off of the height measurement in a direction orthogonal to the scandirection (that is, in the y-direction) as well as the variations in thecorners of the image can be explained by the fixed phase difference inthe embodiment of the in-plane interferometer that gets added to thephase representing the surface topography and the orientation of theGSLM due to motion of the stage. While this fixed phase value would bezero across the field of view if the two objectives 104, 106 wereideally optically matched, in practice it is non-zero. One way toestimate this residual value is to average the phase of each frameduring the x-scan after the resulting phase map is low-pass filtered andthe tip/tilt are removed. The results of such data processing operationis shown in FIG. 10, representing the optical wavefront mismatch betweenthe two arms of the embodiment of the interferometric set-up accordingto the idea of the invention, from which a phase error of themeasurement along the axis perpendicular to the direction of thein-plane scan can be derived. The estimation of such error may beimproved further by forming a phase map of a flat, pattern-freereflector used as a reference SUT, storing the reference data on atangible computer-readable non-transitory medium and then adding thesedata to the estimates of α_(i) obtained from the measurement of thecurrent SUT to further reduce the absolute error in the final phase mapof the currently measured SUT.

In practice, to improve the estimates of a phase map α_(i)(x,y,t)representing the results of the measurement of the surface of theSUT—whether a quasi-continuous surface or a discretized surface such asthat of the SLM—with the embodiments of the in-plane scanninginterferometer of the invention, a phase map may be created for eachimage frame, see FIG. 6A, captured with the camera and a best-fit plane(θ_(x), θ_(y), z) may be found for each image frame. While keeping thesurface of the SUT in focus throughout the scan may be preferred, theabove-described capability of the embodiment to track the slow slopes ofthe SUT surface and/or deviations of it from the focus of the objective104 (which tracking is incomparably slow in comparison with and does notqualify as z-scanning of the vertical scanning interferometer) may beincorporated into one of the embodiments. FIG. 11 illustrates a typical(albeit having a strong noise component due to the use of an inexpensivetranslation stage) z-deviation of the surface of the SUT from its idealposition at the focal plane of the objective 104 (shown in the plot as“mean height” of SUT, also known as z), which can be discovered duringthe scan from one image frame to another.

The width of the coherence envelope, apodizing in practice the intensitydistribution representing the interferometric fringes formed with theuse of a scanning interferometer and, in particular, the reduction ofwidth of such coherence envelop is related to the range of angles atwhich light is incident onto the SUT through the objective of theinterferometer. The limitation of the range of angles of incidence oflight onto the SUT can be attempted with the use of a contraptionschematically illustrated in FIGS. 12A, 12B, and 12C, and will limit thereduction of the coherence envelope width. The spatial spread of light(a range of angles) reflected by the SUT will depend on the spatialfrequencies present in the profile of the surface of the SUT. When thesource is spatially large (for example, an LED source), the lightdistribution it produces in the pupil is spatially-substantial as well,and such source will illuminate the object from many different angles.In this case, the coherence envelope will reduce as a function of z, andpupil filters can be employed.

As shown in FIG. 12A, for example, an optical obscuration unit 1200 isplaced across the substantially collimated input beam of light Larriving from the light source into the embodiments of the in-planescanning interferometer of the invention 1210 (it is appreciated thatoperationally the delivery of light L from a different side of thebeamsplitter of the interferometer 1201 as compared with a relatedembodiment 410 of FIG. 4 does not change the principle of operation ofthe embodiment). Two examples of the optical obscuration unit, 1200A and1200B, are shown respectively in FIGS. 12B and 12C, and contain arespectively—corresponding version of an optically-opaque screen 1214disposed in the plane of an optical diaphragm or aperture 1218. Portionsof each of opaque screens of the embodiments 1200A, 1200B that areoptically-opaque are marked black, while the light-transmitting portionsare shown not colored. Accordingly, the width of the coherence envelopeand, therefore, a degree of coherence of light incident onto the sample100 is controlled by modifying a cross-sectional profile of lightbeamincident onto the sample 100. It is appreciate that generally, theoptical density of at least one of optically-opaque section of thescreen 1214 may be spatially uniform (that is, the value of it is thesame at any point of the optically-opaque section of the screen) ornon-uniform (when the value of optical density at a first point ofoptically-opaque portion of the screen differs from the value of opticaldensity at a second point of optically-opaque portion of the screen).

Possible additional operational differences arising from the use ofincarnations 1200A and 1200B of the obscuration unit stem from theconversion of the path difference into difference in height (surfaceprofile), performed by the embodiment of the invention, which depends onthe combined effects of the incident light at all angles. If the centralportion of light input into the interferometer is fully blocked (as itwould be with the implementation 1200A, then the sensitivity of theembodiment of the system to changes in height of the surface of the SUTis bit higher because the off-axis light experiences a larger pathdifference due to the non-normal incidence. With the use of theimplementation 1200B, on the other hand, the axial (central) portion ofthe light input L is transmitted through towards the in-planeinterferometer, and the net sensitivity is slightly reduced afteraveraging in the effects attributed to the on-axis light.

It is appreciated, therefore, that the proposed methodology employs alateral scanning interferometric apparatus and procedure in which,rather than scanning the test sample or reference mirror along theoptical axis to achieve traditional vertical phase-shifting, thereference mirror is tilted with respect to the optical axis to introducetilt fringes across the field of view. Then, the test sample is scannedalong the x-axis relative to the optical system. The phase shifting isdone by examining the SUT at multiple locations during the scan and withdifferent fringe phases, caused by the interferometric tilt fringes. Theproposed technique allows the entire SUT to be measured incomparablyfaster (by at least 1 or 2 orders of magnitude or more) than withtraditional step and z-phase shift methods. At the same time, inoperation, the need in angle-calibration inevitably present in lateralscanning white-light interferometry is avoided by configuring the systemof the such that angular tilt between the sample objective of theinterferometer and the sample stage (or surface of the SUT beingmeasured) is not present.

In order to ensure a practical range of phase change (of about 3π) formeasurement of a surface profile in a scan direction, it may bepreferred that tilt of the interferometric fringes formed across the SUTby an embodiment of the invention as measured parallel to the directionof scan be no less than about 1.5 fringes. At the same time, the systemis substantially free from any limitation on a phase change in adirection orthogonal to the direction of in-plane or lateral scan.

Continuous scanning of the SUT is effectuated along a scanning direction(discussed herein as x-direction) at a substantially constant velocitywhile camera images are captured at a constant sampling rate, providingthe x-shift accuracy (on the order of 50 nm or so) that substantiallyless constraining operationally than that of about 0.5 nm to 5 nmrequired by a typical vertical scanning phase-shifting system. Inoperation, actual phase steps associated with the SUT surface profilecan be found from the interferometric images acquired with the opticalacquisition system. It is preferred to match the image frame rate of theoptical camera to the scan velocity such that the image of the testedobject is moved by an integer number of camera pixels at each frame.

In operation, the information about a drift of the surface under testfrom the best fit plane (a focal plane of the interferometric objectiveat each camera frame) is optionally used as feedback to a z-repositionerconfigured to keep the sample in focus during the lateral scanningmeasurement in a fashion that does not amount to and cannot be mistakenwith that employed to achieve phase-shifting in a vertical scanninginterferometer. This allows measurement of surfaces with profiledepartures from the focal plane of the objective greater than the depthof field (DOF) of the objective as long as such departures are notabrupt. In the present context, the term “abrupt” implies that thesurface being measured does not have or is devoid of spatialdiscontinuities or steps larger than a quarter of the mean wavelength oflight used to perform the measurement according to an embodiment andthat, as a result of it, there is no 2pi phase ambiguity involved in thedetermination of the phase map. Alternatively or in addition, this termimplies that even when the surface is spatially-continuous, its slope isnot so large that light incident on it through the objective and thenreflected misses (avoids) the numerical aperture of the microscopeobjective and is not captured by the sample arm of the interferometer.

In-plane scanning systems configured according to the idea of theinvention facilitate surface profilometry at least in two measurementmodes:

In one mode, directly producing a topography map of a SUT that is eitherunchanged or is operationally discreet and can be varied betweendifferent surface states (such as in the case of a MEMS-based device),the SUT is characterized in a state in which the surface is at the timeof the measurement, without any changes to the surface, the heightprofile of a given location at the surface is determined relative tothose at other locations across the surface. Here, correction for a“fixed OPD” error between the two arms of the interferometer may beemployed, which includes (i) measurements along the direction of thein-plane scan and in an orthogonal direction in the same plane and/or(ii) calibration of the OPD error between interferometer arms.

In another mode, which may be particularly appealing for a measurementof a discreet, operationally-changeable surface such as that of aMEMS-based device, each location on the test sample is characterizedrelative to itself in two “opposite” or “negative to one another” statesof such location (as defined by the operational states of an individualmirror of the MEMS-based device). Here, image frames obtained from thesame location in two operationally-distinct states of the location areused to produce two phase maps of the test sample that are thereaftercompared to assess the surface profile of the sample and, in particular,assess the change in height of element(s) of an SUT; these can be takenas 2 independent measurement scans, one at each state, or they can beinterleaved in time, with every other frame representing one state, andthe other camera frames measuring the second state.

A person of skill in the art will readily appreciate, upon reading thisdisclosure, that embodiments are particularly fit for measurements of astructure with spatially-varying reflectivity. Indeed, since allmeasurement samplings or readings used to measure the surface height orz position at a given SUT location are made at that same location on theSUT, all of them are subject to the same surface reflectivity figure. Asa result, the reflectivity value cancels out during the LSPSIcalculation and no additional errors are introduced.

It is also appreciated that in a case when the scan axis is not parallelto the x-axis of the imaging camera, the image would drift slightly inthe y-direction as consecutive image frames are taken along thex-direction, which can cause image blurring. In practice, substantialparallelism between these two axes should preferably be maintained overthe extent corresponding to the FOV of the objective and not necessarilythe total extent of the SUT, to achieve the desired results.

It is appreciated that an embodiment of the invention can be operated asa stand-alone tool and/or inspection system or, in the alternative, aspart of the inspection sub-system in line with the system configured tofabricate the devices of interest (such as, for example, MEMS-baseddevices). In one specific case, an embodiment of the invention may beconfigured as an in-line inspection tool of a lithographic exposure toolor apparatus. To this end, the following provides a general descriptionof an example of such exposure tool.

Exposure Apparatus.

An example of an exposure apparatus (also interchangeably referred to asa lithographic apparatus), which may employ an autofocus system (AFS)for measurements of wafer displacements is provided, for example, inPCT/US2012/043186, which is incorporated herein by reference. FIG. 13schematically illustrates, in reference to the provided Cartesian systemof coordinates, a schematic illustration of such exposure apparatus.

The exposure apparatus 1300 includes an apparatus frame 1312, anillumination system 1314 (also referred to as irradiation apparatus), anoptical assembly 1316, a reticle stage assembly 1318, a wafer stageassembly 1320, a positioning system (shown as a combination of severalunits including systems 1322A, 1322B, 1322C), and a control system 1324.The design of the components of the exposure apparatus 1300 can bevaried to suit specific requirements. The exposure apparatus 1300 may bemounted to/on a mounting base 1302, such as the ground, a base, orfloor, or some other supporting structure.

Apparatus Frame. The apparatus frame 1312 is rigid and supports and/orhouses at least the reticle stage assembly 1318, the optical assembly1316, the wafer stage assembly 1320, and the illumination system 1314above the mounting base 1302.

Illumination System. The illumination system 1314 includes anillumination source 1340A and an illumination optical assembly 1340B.The illumination source 1340A emits radiation to which thewafer/work-piece 1328 is exposed and which is guided by the illuminationoptics of the assembly 1340B to the optical assembly 1316, along anoptical axis 1316A. On its way to the optical assembly 1316, the beam ofradiation illuminates a portion of the reticle 1326 to gain spatialpattern of irradiation representing the pattern of the reticle 1326.

The illumination source 1340A can be, for example, any of a g-linesource (436 nm), an i-line source (365 nm), a KrF excimer laser (248nm), an ArF excimer laser (193 nm), a F2 laser (157 nm), or an EUVsource (13.5 nm). The wafer-illuminating (exposure) light may beprovided at about 193 nm (by an ArF excimer laser system, for example)light (with a wavelength of 193 nm), but it can also include ultravioletlight such as described in, for example, U.S. Pat. No. 7,023,610. Thesource 1340A of illuminating light may exploit harmonic frequencyconversion or utilize an optical-fiber based amplifier, to produceradiation at a predetermined wavelength. Alternatively, the illuminationsource 140A can generate charged particle beams such as an x-ray or anelectron beam. For instance, in the case where an electron beam is used,thermionic emission type lanthanum hexaboride (LaB6) or tantalum (Ta)can be used as a cathode for an electron gun. Furthermore, in the casewhere an electron beam is used, the structure could be such that eithera mask is used or a pattern can be directly formed on a substratewithout the use of a mask.

Optical Assembly. The optical assembly 1316 projects and/or focuses thelight passing through the reticle 1326 onto the work piece (wafer) 1328.Depending upon the design of the exposure apparatus 1300, the opticalassembly 1316 can scale (i.e., to magnify or reduce, with a specificcoefficient) dimensions of the pattern of the reticle 1326. In aspecific implementation, the optical assembly 1326 may simply relay thepattern of the reticle 1326 onto the wafer (i.e., have a unitmagnification).

Reticle Stage Assembly. The reticle stage assembly 1318 holds andpositions, (with the use of a reticle stage mover assembly 1318B) thereticle stage 1138A that retains the reticle 1326 relative to theoptical assembly 1316 and the wafer 1328. The reticle stage moverassembly 1318B can be designed to move the reticle stage 1318A along anyof the x, y, z axes.

Wafer Stage Assembly. The wafer stage assembly 1320 holds and positions(with the use of a wafer stage mover 1320B) the wafer 1328 with respectto the image of the illuminated portion of the reticle 1326 projectedonto the wafer. The wafer stage mover 1320B can be designed to move thewafer 1328 along any of the x, y, z axis. In one embodiment, the wafer128 can be scanned while the wafer stage assembly 1320 moves the wafer128 along the y-axis.

Positioning System. The positioning system (1322A, 1322B, 1322C)monitors movement of the reticle 1326 and the wafer 1328 relative to theoptical assembly 1316 or some other reference. As shown in FIG. 13, theposition system 1322 includes (i) an AFS 1322A that maps the topographyof the wafer 1328 relative to the optical assembly 1316 along the Z axis(which is collinear with the optical axis 1316A), about the X axis, andabout the Y axis prior to exposure of the wafer with improved accuracy;(ii) a reticle measurement system 1322B (only a portion of which isillustrated) that monitors the position of the reticle stage 1318A andthe reticle 1326; and (iii) a wafer measurement system 1322C (only aportion of which is illustrated) that monitors the position of the waferstage 1320A along the X and Y axes, and about the Z axis. Due tooperation of the position system, the wafer stage assembly 1320 can becontrolled to position the wafer 1328 with improved accuracy. Thepositioning system 1322 can utilize laser interferometers, encoders,autofocus systems, and/or other measuring devices.

One known implementation the autofocus system 1322A includes a referencesystem 1336 providing a reference signal used in conjunction with andrelated to the measurement of any changing operational parameter of theAFS 1322A but not the position of the wafer 1328 along the optical axis1316A. The AFS 1322A further includes a measurement system 1338, whichprovides a measurement signal used in conjunction with and related tothe measurement of anything changing in the AFS 1322A including (thechange of, if present,) position of the wafer 1328 along the opticalaxis 1316A. By comparing the reference and measurement signals, theposition of the wafer 1328 is measured, which is accompanied withreduction of the stability requirements for many of the components ofthe AFS 1322A.

A typical measurement system 1338 may include an encoder assembly (notshown) that measures, in operation, the position of a work piece (asshown—the wafer 1328). For example, in some embodiments, the encoderassembly can be designed to monitor and/or measure the position of thework piece along two axes (e.g., along the x- and y-axes). Additionallyand/or alternatively, the encoder assembly can be designed to measureand/or monitor the position of the work piece 1328 along all three axes(i.e., to specify the 3D position of the work piece 1328).

The conventional measurement system 1338 may also include a stagegrating (not shown) that is secured to a side of the wafer stage 1320A(of the assembly 1320) that retains the work piece 1328, and one or morefixed encoder heads (not shown). The number of encoder heads and theirmutual positioning and orientation can be varied according to the designof the exposure apparatus 1300 and/or the measurement system 1338, andthe amount of travel of the stage 1320A along x- and y-axes. The use ofmultiple encoder heads enables the encoder assembly to more accuratelymeasure the position of the stage 1320A, and thus the position of thework piece 1328 that is retained by the stage 1320A. Examples of thestructure(s) of the measurement system 1338 and encoder head(s) arediscussed in detail in U.S. 2014/0049762, which is incorporated hereinby reference, and will not be addressed here additionally.

Control System. The control system 1324 is operably connected to andgoverns the operation of at least the illumination system 1314, thereticle stage assembly 1318, the wafer stage assembly 1320, and thepositioning system 1322. The control system 1324 acquires measurementdata, from the positioning system 1322, that represent position and/ororientation and/or movement of the reticle 1326 and/or wafer 1328 withrespect to the optical assembly 1316 or another chosen reference. Basedon these data, the control system 1324 controls the assemblies 1318,1320 to precisely position the reticle 1326 and the wafer 1328. Thecontrol system 1324 can include one or more processors and electroniccircuits, at least one of which may be specifically programmed toperform steps of data acquisition, data processing, and control ofoperation of the components of the apparatus 1300.

Generally, the exposure apparatus 1300 can be used as a scanning typephotolithography system for optical transfer of a spatial pattern fromthe reticle 1326 onto the wafer 1328, with the reticle 1326 and thewafer 1328 moving synchronously. Alternatively, the exposure apparatus1320 can be used as a step-and-repeat type photolithography system thatexposes the reticle 1326 while the reticle 1326 and the wafer 1328 arestationary. The use of the exposure apparatus 1300, however, is notlimited to a photolithography system for semiconductor manufacturing andcan include, as a non-limiting example, the use as an LCDphotolithography system that projects a liquid crystal display devicepattern onto a rectangular glass plate or a photolithography system formanufacturing of a thin film magnetic head.

Fringe-Projection AFS. As is understood by a skilled artisan, theprinciple of operation of a fringe-projection AFS (FP AFS) used inrelated art as part of the exposure apparatus is based on projecting(imaging of) a chosen irradiance pattern formed with the use of thediffraction grating onto the target surface under test (for example, asurface of a semiconductor wafer being measured) and the followingre-imaging an fringe pattern formed on the surface onto an plane of theoptical detector. Such imaging and re-imaging facilitate thedetermination of both the initial (or nominal) position of the surfaceand its new position (for example that resulting from the movement ofthe surface along a line normal to its surface) based on changes of thefringe-pattern formed on the optical detector, which is opticallyconjugate with the surface of the wafer. For detailed discussion of anexample of the AFS the reader is referred to our prior applications, forexample to Ser. No. 14/808,197 published as US 2016/0025480, thedisclosure of which is incorporated herein by reference. Additionaldetails of embodiments of a typical fringe projection AF system and itsoperation in the exposure apparatus can be found in, for example,commonly assigned U.S. Patent Application Publications 2011/0071784 and2012/0008150, as well as the patent application publication WO2012/177663, the disclosure of each of which is incorporated herein byreference. FIG. 2F provides another schematic illustration of the FP-AFSused in the related art (where the fringe-projection portion is shown toinclude the diffraction grating of the AFS.)

For the purposes of this disclosure and the appended claims, the use ofthe terms “substantially”, “approximately”, “about” and similar terms inreference to a descriptor of a value, element, property orcharacteristic at hand is intended to emphasize that the value, element,property, or characteristic referred to, while not necessarily beingexactly as stated, would nevertheless be considered, for practicalpurposes, as stated by a person of skill in the art. These terms, asapplied to a specified characteristic or quality descriptor means“mostly”, “mainly”, “considerably”, “by and large”, “essentially”, “togreat or significant extent”, “largely but not necessarily wholly thesame” such as to reasonably denote language of approximation anddescribe the specified characteristic or descriptor so that its scopewould be understood by a person of ordinary skill in the art. In onespecific case, the terms “approximately”, “substantially”, and “about”,when used in reference to a numerical value, represent a range of plusor minus 20% with respect to the specified value, more preferably plusor minus 10%, even more preferably plus or minus 5%, most preferablyplus or minus 2% with respect to the specified value. As a non-limitingexample, two values being “substantially equal” to one another impliesthat the difference between the two values may be within the range of+/−20% of the value itself, preferably within the +/−10% range of thevalue itself, more preferably within the range of +/−5% of the valueitself, and even more preferably within the range of +/−2% or less ofthe value itself.

The use of these term in describing a chosen characteristic or conceptneither implies nor provides any basis for indefiniteness and for addinga numerical limitation to the specified characteristic or descriptor. Asunderstood by a skilled artisan, the practical deviation of the exactvalue or characteristic of such value, element, or property from thatstated falls and may vary within a numerical range defined by anexperimental measurement error that is typical when using a measurementmethod accepted in the art for such purposes.

For example, a reference to an identified vector or line or plane beingsubstantially parallel to a referenced line or plane is to be construedas such a vector or line or plane that is the same as or very close tothat of the referenced line or plane (with angular deviations from thereferenced line or plane that are considered to be practically typicalin related art, for example between zero and fifteen degrees, preferablybetween zero and ten degrees, more preferably between zero and 5degrees, even more preferably between zero and 2 degrees, and mostpreferably between zero and 1 degree). For example, a reference to anidentified vector or line or plane being substantially perpendicular toa referenced line or plane is to be construed as such a vector or lineor plane the normal to the surface of which lies at or very close to thereferenced line or plane (with angular deviations from the referencedline or plane that are considered to be practically typical in relatedart, for example between zero and fifteen degrees, preferably betweenzero and ten degrees, more preferably between zero and 5 degrees, evenmore preferably between zero and 2 degrees, and most preferably betweenzero and 1 degree). For example, a term “substantially-rigid”, when usedin reference to a housing or structural element providing mechanicalsupport for a contraption in question, generally identifies thestructural element that rigidity of which is higher than that of thecontraption that such structural element supports. As another example,the use of the term “substantially flat” in reference to the specifiedsurface implies that such surface may possess a degree of non-flatnessand/or roughness that is sized and expressed as commonly understood by askilled artisan in the specific situation at hand. Other specificexamples of the meaning of the terms “substantially”, “about”, and/or“approximately” as applied to different practical situations may havebeen provided elsewhere in this disclosure.

References throughout this specification to “one embodiment,” “anembodiment,” “a related embodiment,” or similar language mean that aparticular feature, structure, or characteristic described in connectionwith the referred to “embodiment” is included in at least one embodimentof the present invention. Thus, appearances of the phrases “in oneembodiment,” “in an embodiment,” and similar language throughout thisspecification may, but do not necessarily, all refer to the sameembodiment. It is to be understood that no portion of disclosure, takenon its own and in possible connection with a figure, is intended toprovide a complete description of all features of the invention.

In addition, it is to be understood that no single drawing is intendedto support a complete description of all features of the invention. Inother words, a given drawing is generally descriptive of only some, andgenerally not all, features of the invention. A given drawing and anassociated portion of the disclosure containing a descriptionreferencing such drawing do not, generally, contain all elements of aparticular view or all features that can be presented is this view, forpurposes of simplifying the given drawing and discussion, and to directthe discussion to particular elements that are featured in this drawing.A skilled artisan will recognize that the invention may possibly bepracticed without one or more of the specific features, elements,components, structures, details, or characteristics, or with the use ofother methods, components, materials, and so forth. Therefore, althougha particular detail of an embodiment of the invention may not benecessarily shown in each and every drawing describing such embodiment,the presence of this detail in the drawing may be implied unless thecontext of the description requires otherwise. In other instances, wellknown structures, details, materials, or operations may be not shown ina given drawing or described in detail to avoid obscuring aspects of anembodiment of the invention that are being discussed. Furthermore, thedescribed single features, structures, or characteristics of theinvention may be combined in any suitable manner in one or more furtherembodiments.

The operation of embodiments of the invention has been described asincluding a specifically-programmed computer-readable processorcontrolled by instructions stored in a tangible, non-transitory storagememory. The memory may be random access memory (RAM), read-only memory(ROM), flash memory or any other memory, or combination thereof,suitable for storing control software or other instructions and data.Instruction information may be conveyed to a processor throughcommunication media, including wired or wireless computer networks. Inaddition, while the invention may be embodied in software, the functionsnecessary to implement the invention may optionally or alternatively beembodied in part or in whole using firmware and/or hardware components,such as combinatorial logic, Application Specific Integrated Circuits(ASICs), Field-Programmable Gate Arrays (FPGAs) or other hardware orsome combination of hardware, software and/or firmware components.

Disclosed aspects, or portions of these aspects, may be combined in waysnot listed above. Accordingly, the invention should not be viewed asbeing limited to the disclosed embodiment(s).

What is claimed is:
 1. A method for profiling a surface, the methodcomprising: determining a height profile of the surface based on phasesof light distribution, formed in reflection of light by the surface withthe use of an interferometer and containing interferometric fringes thatare angularly tilted with respect to a direction of an in-plane scanningof the surface, while the surface is being scanned in said directionperpendicular to an optical axis of a sample arm of the interferometerin absence of angular inclination between said optical axis and a linethat is perpendicular to the surface, wherein said direction is adirection transverse to said interferometric fringes.
 2. A methodaccording to claim 1, wherein a region-of interest (ROI) at said surfacehas an ROI dimension exceeding a dimension of a field-of-view (FOV) ofan objective of the interferometer as defined on the surface by at leasttwo times, wherein said determining is accomplished for all of the ROIin a first time that is smaller than a second time by at least an orderof magnitude, and wherein the second time is a time required todetermine said height profiled for all of the ROI with a verticalscanning interferometer.
 3. A method according to claim 1, furthercomprising scanning said surface in said direction by incrementallyshifting said surface in a plane perpendicular to the optical axis,wherein a shift increment of said scanning is optically conjugate, to aninteger number of pixels of an optical detector configured to acquiresaid light distribution, in an optical system containing saidinterferometer.
 4. A method according to claim 1, comprising tilting areference reflector in a reference arm of the interferometer to form atleast 1.5 of said interferometric fringes across a field-of-view (FOV)of an objective in a reference arm of said interferometer.
 5. A methodaccording to claim 1, configuring the interferometer to define an angleof tilt between said interferometric fringes and said direction to bedifferent from zero.
 6. A method according to claim 1, furthercomprising changing a width of an apodization curve limiting thedistribution of intensity of said interferometric fringes andrepresenting a change in contrast of said interferometric fringes bymodifying a cross-sectional profile of said light delivered to theinterferometer.
 7. A method according to claim 1, wherein saiddetermining includes determining said height profile of the surface thathas been patterned in a lithographic exposure tool, wherein saidinterferometer is in-line with said exposure tool.
 8. An apparatus forprofiling a surface, the apparatus comprising: a beam splitterpositioned to divide a light beam incident thereon into a measurementlight beam and a reference light beam directed along a reference axis; areference reflector positioned in an optical path of the reference lightbeam, the reference reflector being inclined with respect to thereference axis; and a repositioning system configured to change, duringsaid profiling, a first positional relationship between a component ofthe apparatus and the surface along a repositioning axis; wherein saidbeam splitter is configured to direct said measurement light beamtowards the surface to irradiate said surface and form a reflectedmeasurement light beam, said reflected measurement light beam passingthrough the beam splitter to interfere with the reference light beamupon reflection thereof from the reference reflector, and wherein saidrepositioning axis extends transversely to an interference fringeformed, during said profiling, on an output side of said beam splitter.9. An apparatus of claim 8, wherein a normal to the reference reflectorcrosses the reference axis.
 10. An apparatus of claim 8, furthercomprising: a measurement objective disposed between the beam splitterand the surface to converge the measurement light beam incident onto themeasurement objective from the beam splitter; and a reference objectivedisposed between the beam splitter and the reference reflector toconverge the reference light beam incident onto the measurementobjective from the beam splitter.
 11. An apparatus of claim 8, wherein anormal to the reference reflector is in a plane that contains both thereference axis and the measurement axis.
 12. An apparatus of claim 11,wherein the repositioning axis is defined by a vector that lays in saidplane.
 13. An apparatus of claim 8, further comprising a detectorconfigured to detect light distribution formed as a result of opticalinterference between the measurement light beam and the reference lightbeam.
 14. An apparatus of claim 13, wherein the detector is furtherconfigured to detect the light distribution while the first positionalrelationship between the component of the apparatus and the surface isbeing changed.
 15. An apparatus of claim 13, wherein, during saidprofiling, a) the interference fringe is formed on a detection surfaceof the detector, and b) a second positional relationship between theinterference fringe and the detection surface is being changed while thefirst positional relationship between the component of the apparatus andthe surface is being changed.
 16. An apparatus of claim 13, wherein thedetector is configured to acquire, during said profiling, a plurality oflight distribution images.
 17. An apparatus of claim 16, furthercomprising a programmable processor in operable cooperation with thedetector, the processor configured to generate a spatial profile of thesurface based on information of the plurality of light distributionimages received from the detector.
 18. An apparatus of claim 10, whereinthe apparatus is configured to form, during said profiling, aninhomogeneous light distribution at at least one of i) a pupil of themeasurement objective and ii) a pupil of the reference objective.
 19. Anapparatus for profiling a surface under test, the apparatus comprising:a beam splitter positioned to divide a light beam incident thereon intoa measurement light beam and a reference light beam directed along areference axis; a reference reflector positioned in an optical path ofthe reference light beam, the reference reflector being inclined withrespect to the reference axis; a measurement objective disposed betweenthe beam splitter and the surface to converge the measurement light beamincident onto the measurement objective from the beam splitter; areference objective disposed between the beam splitter and the referencereflector to converge the reference light beam incident onto themeasurement objective from the beam splitter, the beam splitterconfigured to direct said measurement light beam towards the surface toirradiate the surface and form a reflected measurement light beam, thereflected measurement light beam passing through the beam splitter tointerfere with the reference light beam upon reflection of the referencelight beam from the reference reflector, wherein the apparatus isconfigured to form, during said profiling, an inhomogeneous lightdistribution at at least one of i) a pupil of the measurement objectiveand ii) a pupil of the reference objective.